Geodesic
On ranks of subsets in the space of binary vectors admitting an embedding of a~Steiner system $S(2,4,v)$
Prikladnaâ diskretnaâ matematika, no. 1 (2014), pp. 73-76

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A bound for the rank of a subset $X$ in the vector space $\mathbb F_2^n$ is obtained via the covering radius of the code lying in the subspace of linear dependencies of vectors in $X$. Also, an upper bound for the covering radius of a code generated by the incidence matrix of a Steiner system $S(2,4,v)$ is obtained. Precice and asymptotic bounds for the rank of a subset $X$ in the vector space $\mathbb F_2^n$ admitting an embedding of a Steiner system $S(2,4,v)$ are obtained too.
Keywords: rank, affine rank, bounds, linear subspace, linear code, covering radius, Steiner system, Boolean functions, spectrum support. 
@article{PDM_2014_1_a7,
     author = {Y. V. Tarannikov},
     title = {On ranks of subsets in the space of binary vectors admitting an embedding of {a~Steiner} system $S(2,4,v)$},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {73--76},
     publisher = {mathdoc},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2014_1_a7/}
}
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Y. V. Tarannikov. On ranks of subsets in the space of binary vectors admitting an embedding of a~Steiner system $S(2,4,v)$. Prikladnaâ diskretnaâ matematika, no. 1 (2014), pp. 73-76. http://geodesic.mathdoc.fr/item/PDM_2014_1_a7/